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Carl Rothe and John Gersting
The mathematical Model was designed to demonstrate and clarify the
interactions between the heart and peripheral circulation in the development
and control of an adequate cardiac output and systemic arterial blood pressure.
The interactive Tutorial was designed to help your understanding of the
physiology of the circulatory system, including the causes-and-effects
involved with function.
Please Note: A ten-page Descriptive paper and Instructions for downloading the
CVI Project, as zipped files, are available at the American Physiological
Society web site for Advances in Physiology Education at:
Cardiovascular Interactions is an active learning tool that demonstrates the
complex and intricate interactions between the functions of the heart and
peripheral circulation.
This learning package, for both teachers and students, consists of a Lab Book,
a Model, and an Information File.
The Lab Book is an interactive tutorial for exploring the relative influences of
parameter changes on the cardiovascular system. Consequences of heart failure,
hemorrhage, and exercise can also be explored. The results obtained in the Lab
Book are based on the Model used.
The mathematical Model reflects our current understanding of the basic
function of the cardiovascular system. It was designed to be complex enough to be
realistic, yet not so complex as to be overwhelming.
The Model has five compartments including a left ventricle, systemic arterial
bed, venous bed, right ventricle, and a lung bed to represent the major parts of the
cardiovascular system. It includes 15 defining parameters and 32 variables. It is
based on five basic relationships:
1. Conservation of mass related to the difference between inflow, outflow and
the accumulation of stressed volume in a compartment, using differencedifferential equations solved iteratively at 0.001 min intervals;
2. Distending Pressure related to stressed volume and compliance;
3. Flow related to pressure gradient and resistance;
4. Cardiac output as Heart Rate times (End-Diastolic-Volume minus EndSystolic Volume), and
5. Vigor of cardiac contraction related to end-diastolic-volume (Starling’s
Law of the Heart) and end-systolic-pressure (Emax).
An Information File contains definitions and descriptions of key classical
physiology concepts, including figures, and a discussion of the Lab Book
“experiments”. A detailed description of the model and documentation of
parameter values user are included. An Index and Hypertext tags embedded in the
Lab Book provide ready access to the contents of this file.
Both the Information and help file and the Lab Book have a detailed Table of
-o-o-o-o-oDesigned to be run from its CD, the Cardiovascular Interactions learning package
need not be installed on the user’s computer. The downloaded files can be run
from a computer with Microsoft Windows without installation.
Learners Targeted
This project will improve the understanding of the cardio-vascular system at the
total body level for: medical, graduate and bioengineering students and also
Professors, Clinicians, and Scientists who need a clear and consistent grasp of its
The project may be used for:
1. Your review of concepts and the approach of chains of logic through causeand-effect
2. Part of a physiology laboratory course with students discussing and learning
in groups of 2 or 3.
3. Lecture display of only the Model and Data Plot.
4. Alternative to animal laboratory, with student assigned to specific
experiments, predictions expected, questions answered and floppy with Lab
Book submitted to Instructor.
5. Distributed (asynchronous) education tool for topics not covered during
lecture time.
6. Continuing education for anesthesiologists, cardiovascular surgeons,
emergency medicine physicians.
7. Bioengineers needing more physics applied to physiology and an example of
a complex mechanical system with negative feedback control.
Topics included for helping the Learner:
⇒ Explain the difference between Emax (related to afterload, that is ventricular
end systolic pressure) and the Frank-Starling law of the heart (related to
preload, that is ventricular end diastolic volume) as major determinants of the
vigor of cardiac contraction.
⇒ Explain how a change in each characterizing parameter of the cardiovascular
system, such as resistance, compliance, total stressed volume, vigor of cardiac
contraction, heart rate, or intrathoracic pressure modifies cardiovascular
⇒ Explain why changes in blood volume distribution and vascular capacitance
are important parts of the inherent, hydraulic mechanisms for cardiovascular
⇒ Discover which parameter changes are most effective for providing
compensation for heart failure, vigorous exercise, or hemorrhage.
⇒ Understand why a venous resistance, which provides a difference between
central venous and peripheral venous pressures, is necessary for explaining
the coupling between the heart and peripheral vasculature.
⇒ Explain whether Cardiac output controls Right atrial pressure.
⇒ Explain whether Right atrial pressure controls Venous return.
⇒ Explain why the ventricular ejection fraction, while useful, is not a fully
adequate measure of cardiac contractility.
⇒ Predict conditions under which venous return does not equal cardiac output
and in what direction and why not.
Model Characteristics
The five-compartment mathematical model is simulated by a series of equations
that, in conjunction with the parameters, define the system function and the
magnitude of the variables (e.g. outflow, pressure, and distended volume) of each
The two facets of the Vigor of Cardiac contraction, revealed and emphasized
with the Model, are:
a) The magnitude of preload (the end-diastolic volume that is the basis of the
Frank-Starling Law of the Heart), and
b) The magnitude of afterload (the end-systolic pressure that, with Emax,
determines the end-systolic volume).
Implementation of the Conservation of Mass principle is the key to the utility
and reliability of the model. Using this principle, volume is redistributed
between the five compartments in accordance with the current parameter set used.
The Model demonstrates the concept that mechanical feedback mechanisms
(such as passive blood volume redistribution influence on ventricular preload and
afterload) control the cardiovascular system to reduce the susceptibility to
disturbances that could cause derivations from optimal function.
Experiments for study of Cardiovascular Interactions
Basic Physiology
Change from Normal
1. Arterial Resistance (Vasoconstriction)
200 %.
2. Arterial Resistance (Vasodilation)
50 %
3. Venous Resistance (Venoconstriction)
200 %
4. Venous Compliance
50 %
5. Arterial Compliance
50 %
6. Left Ventricular Contractility
500 %
7. Right Ventricular Contractility
500 %
8. Heart Rate on Stroke Volume and Cardiac Output
(Normal, 18, 48, 144, 216 beats/minute)
9 Unstressed blood volume, venous,
- 500 ml
10. Venous-return : Cardiac-output relationship.
Pathophysiology and Stress
11 Left Heart Failure via Emax
15 %
Congestive Left Heart Failure + Blood volume+ 750 ml
Congestive Right and Left Heart Failure compared
Intrathoracic pressure (Pit)
- 4 to 0 mmHg
Blood volume -1750 ml
Suggest effective compensatory changes to mimic fluid shifts and reflex
control of the cardiovascular system following hemorrhage.
16. Hypertension with arteriosclerosis
Ra = 150%
and Ca 50 %.
Ra is arterial resistance Ca is arterial compliance
17. Exercise
Ra = 20 %
Explore and describe effective compensatory changes that act to maintain
arterial blood pressure while providing a cardiac output of several times
normal during vigorous skeletal muscle exercise.
18. Experimental Test Bed.
To use the Model without the Tutorial
A major revision is underway. A pulmonary venous compartment has been added. The
user will be able to develop and use their own parameter set, and separately control right
and left ventricular heart rate.
CVI Project availability:
1) On a CD from Professor Rothe
2) As zipped files from the APS Web page
Descriptive papers:
Rothe, C.F. and Gersting, J.M. “Cardiovascular Interactions: An interactive
tutorial and mathematical model.” Advances in Physiology Education 29:98109, 2002.
Gersting, J.M. and Rothe. C.F. “Cardiovascular Interactions Tutorial: Architecture
and Design.” J. Medical Systems 26:29-38, 2002
Copyright 2002 by Carl F. Rothe
Permission is hereby granted to reproduce and distribute copies of this work for nonprofit
educational purposes, provided that copies are distributed at or below cost, and that the author,
source, and copyright notice are included on or in each copy.